Pebble Trapping in Vortices: Three-dimensional Simulations
Natalie Raettig, Wladimir Lyra, Hubert Klahr
Abstract
Abstract Disk vortices have been heralded as promising routes for planet formation due to their ability to trap significant amounts of pebbles. While the gas motions and trapping properties of two-dimensional vortices have been studied in enough detail in the literature, pebble trapping in three dimensions has received less attention, due to the higher computational demand. Here we use the Pencil Code to study 3D vortices generated by convective overstability and the trapping of solids within them. The gas is unstratified whereas the pebbles settle to the midplane due to vertical gravity. We find that for pebbles of normalized friction times of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>St</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.05</mml:mn> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>St</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> , and dust-to-gas ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ε</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.01</mml:mn> </mml:math> , the vortex column in the midplane is strongly perturbed. Yet when the initial dust-to-gas ratio is decreased the vortices remain stable and function as efficient pebble traps. Streaming instability is triggered even for the lowest dust-to-gas ratio ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ε</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:math> ) and smallest pebble sizes ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>St</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.05</mml:mn> </mml:math> ) we assumed, showing a path for planetesimal formation in vortex cores from even extremely subsolar metallicity. To estimate if the reached overdensities can be held together solely by their own gravity we estimate the Roche density at different radii. Depending on disk model and radial location of the pebble clump we do reach concentrations higher than the Roche density. We infer that if self-gravity was included for the pebbles then gravitational collapse would likely occur.